SURVEY ARTICLE

Semigroups with certain finiteness conditions and Chernikov groups

L. N. Shevrin

Institute of Mathematics and Computer Science, Ural Federal University, Lenina 51, 620083 Ekaterinburg, Russia

Abstract: The main purpose of this short survey is to show how groups of special structure, which are accepted to be called Chernikov groups, appeared in the considerations of semigroups with certain finiteness conditions. A structure of groups with several such conditions has been described (they turned out to be special types of Chernikov groups). Lastly, a question concerning some special type of Chernikov groups is recalled; this question was raised by the author more than 35 years ago, and it is still open.

Keywords: finiteness condition, epigroup, finitely assembled semigroup, Chernikov group.

Received: 07.05.2012
Revised: 18.05.2012

Language: English

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